It just takes away the mental overhead of making something conform to a spec. It probably doesn't save us much on production bugs, but it makes development faster.
1. If they're using a dynamically typed language, this gives them extra work to typecast everything back and forth whenever they need to communicate with your system.
2. Even if they use types, maybe their type system is not compatible with yours and they need to do a lot of tedious extra work to typecast everything.
I treat other systems like I do the database and enforce consistency at the API level.
I wouldn't ask for a database to be totally untyped (and thus silently coerce things into its internal types in reality), so I don't ask for the same in an API.
Though, I can understand some people have differing preferences---MongoDB is popular for example---but I wouldn't call it an anti-pattern no matter which choice one makes.
I have never found option 2 to apply in any meaningful fashion, though I'm sure others have done much more of this type of work than I have.